A Beam is a structural element that is capable of withstanding load
primarily by resisting against bending. Beams are characterized by
their second moment of area, their length and their elastic modulus.

In Sympy, we can construct a 2D beam objects with the following properties :

Length

Elastic Modulus

Second Moment of Area

Variable : A symbol that can be used as a variable along the length. By default,
this is set to Symbol(x).

A beam of length 9 meters is having a fixed support at the start.
A distributed constant load of 8 kN/m is applied downward from the starting
point till 5 meters away from the start. A clockwise moment of 50 kN-m is
applied at 5 meters away from the start of the beam. A downward point load
of 12 kN is applied at the end.

Note

Since a user is free to choose its own sign convention we are considering
the upward forces and clockwise bending moment being positive.

There is a beam of length 30 meters. A moment of magnitude 120 Nm is
applied in the clockwise direction at the end of the beam. A pointload
of magnitude 8 N is applied from the top of the beam at the starting
point. There are two simple supports below the beam. One at the end
and another one at a distance of 10 meters from the start. The
deflection is restricted at both the supports.

Note

Using the sign convention of upward forces and clockwise moment
being positive.

A beam of length 6 meters is having a roller support at the start and a
hinged support at the end. A clockwise moment of 1.5 kN-m is applied at the mid
of the beam. A constant distributed load of 3 kN/m and a ramp load of 1 kN/m
is applied from the mid til the end of the beam.

Note

Using the sign convention of upward forces and clockwise moment
being positive.